Summary: Intersection Types and Lambda Models
Fabio Alessi a
a Dip. di Matematica e Informatica Via delle Scienze, 206
33100 Udine (Italy) alessi@dimi.uniud.it
Franco Barbanera b
b Dip. di Matematica e Informatica Viale A.Doria, 6
95125 Catania (Italy) barba@dmi.unict.it
Mariangiola Dezani­Ciancaglini c
c Dip. di Informatica Corso Svizzera, 185
10149 Torino (Italy) dezani@di.unito.it
Research Report UDMI/06/2004/RR
Abstract
The invariance of the meaning of a ­term by reduction/expansion w.r.t. the considered
computational rules is one of the minimal requirements for a ­model. Being the intersec­
tion type systems a general framework for the study of semantic domains for the Lambda­
calculus, the present paper provides a characterisation of ``meaning invariance'' in terms of
characterisation results for intersection type systems enabling typing invariance of terms
w.r.t. various notions of reduction/expansion, like , and a number of relevant restrictions
of theirs. Building on these results, the paper provides also necessary and sufficient condi­
tions an (intersection) filter ­structure needs to satisfy in order to be models of (restricted)